Question

$ A_{(g)} \xrightarrow{\Delta} P_{(g)} + Q_{(g)} + R_{(g)}$, follows first order kinetics with a half life of $69.3\, s$ at $500^\circ\,C$. Starting from the gas $'A'$ enclosed in a container at $500 ^\circ\,C$ and at a pressure of $0.4 \,atm$, the total pressure of the system after $230\, s$ will be

• A. 1.32 atm
• B. 1.12 atm
• C. 1.15 atm
• D. 1.22 atm

Answer 1

Answer: (B)

$p_{t} =(0.4-x)+x +x +x$

$=0.4+2 x$

or $x=\frac{p_{t}-0.4}{2}$

$\therefore p_{A}=p_{0}-x =p_{0}-\frac{p_{t}-0.4}{2}$

$=\frac{2 \times 0.4-p_{t}+0.4}{2}$

$=\frac{1.2-p_{t}}{2}$

From $k=\frac{2.303}{t} \log \left(\frac{p_{0}}{p_{A}}\right)$

$\frac{0.693}{t_{1 / 2}} =\frac{2.303}{230} \log \left(\frac{0.4 \times 2}{1.2-p_{t}}\right)$

$\frac{0.693}{69.3} =\frac{2.303}{230} \log \left(\frac{0.8}{1.2-p_{t}}\right)$

$\log \left(\frac{0.8}{1.2-p_{t}}\right) =\frac{0.693 \times 230}{69.3 \times 2.303}$

$=0.9987$

$\frac{0.8}{1.2-p_{t}} =$ antilog (0.9987)

$\frac{0.8}{1.2-p_{t}} \approx 10$

$\therefore 12-10 p_{t} =0.8$

or $p_{t} =1.12\, atm$